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Marine Geo logy , 60 (1984) 455--473 455Elsevier Science Publishers B.V., Amsterdam --Printed in The Netherlands

R E C O N S T R U C T I O N O F A N C I E N T S E A C O N D I T I O N S W IT H A NE X A M P L E F R O M T H E S W IS S M O L A S S E

P H I L I P A . A L L E ND epa r tm en t o f Geo logy , U nivers i ty Co llege , P .O . Bo x 78, Card i f f CF1 1XL (U ni tedK i n g d o m )(Received March 15, 1983; revised and accepted August 29, 1983)

A B S T R A C TA l l e n , P . A . , 1 9 8 4 . R e c o n s t r u c t i o n o f a n c i e n t s e a c o n d i t i o n s w i t h a n e x a m p l e f r o m t h e

S w i s s M o l a s s e . I n : B . G r e e n w o o d a n d R . A . D a v i s , J r. ( E d i t o r s ) , H y d r o d y n a m i c s a n dS e d i m e n t a t i o n i n W a v e - D o m i n a t e d C o a s t a l E n v i r o n m e n t s . M a r . G e o l . , 6 0 : 4 5 5 - - 4 7 3 .A n c i e n t s e a c o n d i t i o n s c a n b e e s t i m a t e d f r o m t h e g r a i n s i z e , s p a c i n g a n d s t e e p n e s s

o f p r e s e r v e d r i p p l e - m a r k s . T h e e l e m e n t o f g r e a t e s t u n c e r t a i n t y i n s u c h r e c o n s t r u c t i o n s i st h e r e l a t i o n s h i p b e t w e e n n e a r - b e d o r b i t a l d i a m e t e r o f w a t e r p a r t i c l e s a n d t h e r i p p l es p a c i n g . T h i s r e l a t i o n s h i p i s s i m p l e f o r v o r t e x r i p p l e s o f h i g h s t e e p n e s s b u t i s p r o b l e m -a t ic a l f o r t h e l o w - s t e e p n e s s f o r m s k n o w n a s p o s t - v o r t e x , r o ll i ng - g ra i n o r a n o r b i t a l r i pp l es .

T h e e x i s t e n c e f i e l d f o r w a v e r i p p l es i s b e t w e e n t h e t h r e s h o ld v e l o c i t y f o r s e d i m e n tm o v e m e n t a n d t h e o n s e t o f s h e e t f l o w , m o s t l o w - s t e e p n e s s f o r m s o c c u r r i n g c l o s e t o t h eb e d p l a n a t i o n t h r e sh o l d . A r a n g e o f m a x i m u m p e r i o d o f f o r m a t i v e w a v e s c a n b e o b t a i n e du s i n g c o m b i n a t i o n s o f o r b i t a l d i a m e t e r a n d o r b i t a l v e l o c i t y , a s s u m i n g l i n ea r w a v e t h e o r yt o b e a r e a s o n a b l e a p p r o x i m a t i o n .

P r o b a b l e w a v e h e i g h t s , w a v e l e n g t h s a n d w a t e r d e p t h s c a n b e i n v e s t i g a t e d u s i n g t h et r a n s f o r m a t i o n o f w a v e p a r a m e t e r s i n s h a l l ow i n g w a t e r s a n d t h e c o n s t r a i n t s o n w a v ed i m e n s i o n s p r o v i d e d b y t h e w a v e - b r e a k i n g c o n d i t i o n . G i v e n r e a s o n a b l e e s t i m a t e s o fW a v e h e i g h t , c r u d e e s t i m a t e s o f w a v e p o w e r a l l o w a c o m p a r i s o n o f a n c i e n t w a v e -i n f l u e n c e d s e q u e n c e s w i t h m o d e r n c o u n t e r p a r t s .

W a v e r i p p l e - m a r k s p r e s e r v e d i n t h e U p p e r M a r i n e M o l a s s e o f w e s t e r n S w i t z e r l a n d h a v eb e e n i n v e s t i g a te d . R e s u l t s , w h i c h a r e i n a g r e e m e n t w i t h r e g i o n a l g e o l o g y , s u g g e s t d e p o s i -t i o n i n a s e a w a y o f a p p r o x i m a t e l y 1 0 0 k m w i d t h , w h e r e m o d e r a t e p e r i o d w a v e s ( T =3 - - 6 s ) w e r e g e n e r a t e d . T h e d e p o s i t i o n a l f a c ie s b e l t s w e r e a d j u s t e d t o t h e p r e v a i l i n g w a v e s ,t i d e s a n d f l uv i a l o u t f l o w s .I N T R O D U C T I O N

S i nc e H a r m s ( 1 9 6 9 ) , T a n n e r ( 1 97 1 ) a n d K o m a r ( 1 9 7 4 ) , w i t h v a ry i ngdegrees of rigour, pro pos ed the use of preserved w~ ve ripple-marks in re-constructing ancient wav e conditions, surprisingly few ancie nt sequenceshave been analysed in this way. Further encourag ements both fro m theo-retical an d empirical (Clifton, 19 76 ; Allen, 1979; Dingler, 197 9; Miller an dKo ma r, 1980a) and field studies (Newto n, 1968; C o o k and Gorsline, 1972;S t o n e a n d S u m m e r s , 1 9 72 ; D i ng l er a n d I n m a n , 1 9 7 7 ; Mi l le r a n d K o m a r ,19 80 b) have no t yet resulted in a flourish of case-studies f ancien t ma ri ne0 0 2 5 - 3 2 2 7 / 8 4 / $ 0 3 . 0 0 1 9 8 4 E l s e v i e r S c i e n c e P u b l i s h e r s B . V .

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o r l a c u s t r i n e s e d i m e n t a r y b a s i n s . A l l e n ( 1 9 8 1 a ) a n a l y s e d a D e v o n i a n l a cu s -t r i n e b a si n- fi ll a n d H o m e w o o d a n d A l l e n ( 1 9 8 1 ) s t u d i e d t h e m a r i n e s ed i-m e n t s o f t h e " U p p e r M a ri n e M o l as s e" o f S w i t z e rl a n d , b u t t o t h e a u t h o r ' sk n o w l e d g e v er y f e w o c e a n i c c o a s t li n e d e p o s i t s h a v e b e e n c o m p r e h e n s i v e l yt r e a t e d .T h e r e a re , o f c o u r s e, f o r m i d a b l e as s u m p t i o n s a n d a p p r o x i m a t i o n s w h i c hm u s t b e m a d e i n q u a n t i fy i n g a n c i e n t w a v e c o n d i t i o n s (A l le n , 1 9 8 1 b ) , b u tw i t h k n o w l e d g e o f t h e p i tf al ls , i m p o r t a n t i n s ig h ts i n to p a l a e o e n v i r o n m e n t sa n d p r o c e ss e s c a n b e a c q u i r e d . W i t h o u t k n o w l e d g e o f t h e a s s u m p t i o n sa n d a p p r o x i m a t i o n s , s p u r i o u s r e s u lt s w i ll b e o b t a i n e d . T h e p u r p o s e o f t h i sp a p e r is t o d e s c ri b e t h e m e t h o d s u s e d b y H o m e w o o d a n d A l le n ( 1 9 8 1 ) int h e i r a n a l y si s o f t h e U p p e r M a r i n e M o la s se o f w e s t e r n S w i t z e r l a n d a n d tos y n t h es i ze s o m e o f t h e m o r e i m p o r t a n t e l e m e n t s o f p a r t ic u l a r u n c e r t a i n t yi n t h e r e c o n s t r u c t i o n o f a n c i e n t s ea c o n d i ti o n s . T h i s c o n t r i b u t i o n t h e r e f o r ea c ts a s s o m e t h i n g o f a c o o k b o o k w h i c h m a y e n c o u r a g e w o r k e r s to a n al y se o rr e -a n a ly s e q u a n t i t a t i v e l y t h e i r a n c i e n t w a v e - i n f l u e n c e d s e q u e n c e s .METHODS

A r e t h e y w a v e r i p p le - m a r k s ?B o e r s m a ( 1 9 7 0 ) d i s ti n g u i sh e d a n u m b e r o f f e a tu r e s t h o u g h t to b e c ha ra c-t e r i s t ic o f w a v e - g e n e r a t e d r ip p l e c r o s s - l a m i n a t i o n , i n c l u d i n g i r r eg u l a r o rc a t e n a r y - a r c u a t e l o w e r b o u n d i n g s u r fa c es , b u n d l e d u p b u i l d i n g o f cr o ss -s e ts

w i t h i n r i p p l e c r o s s - l a m i n a t e d l en s e s , c h e v r o n s t r u c t u r e s , c r o s s - s tr a t al o f f -s h o o t s a n d f o r m - d i s c o r d a n c y . T a n n e r { 1 9 6 7) a n d R e i n e c k e t a l. ( 1 9 7 1 )l ik e w i s e s u m m a r i z e d w a v e ri p p l e - m a r k s in t e r m s o f ri p p l e s t ee p n e s s , s y m -m e t r y a n d c r es t al a r r a n g e m e n t i n p l an . W a v e r i p p l e -m a r k s c h a r a c t er i st i c al l yh a v e s t r a i g h t c r e s t l i n e s w h i c h c o m m o n l y b i f u r c a t e , l o w r i p p l e i n d i c e s a n ds y m m e t r i c a l t o n e a r - s y m m e t r i c a l p r o f il e s.T h e r e h a v e b e e n r e l a ti v e l y f e w s t u d i e s o f t h e n a t u r a l v a ri a b i l it y in m o r -p h o l o g y a n d s t r u c t u r e o f w a v e r i p p l e -m a r k s . A v e ry w i d e s p e c t r u m o f r i p p l em o r p h o l o g i e s h a s b e e n d e s c r ib e d f r o m e x p e r i m e n t a l st u d ie s ( B a g n o ld , 1 9 4 6 ;M a n o h a r , 1 9 5 5 ; D i n g i er , 1 9 7 4 ; S l e a th , 1 9 7 6 ) , r a n g in g f r o m t h e v e r y f i a tv a r i e t i e s w h i c h h a v e v a r i o u s l y b e e n t e r m e d " r o l l i n g g r a i n r i p p l e s " ( B a g n o l d ,1 9 4 6 ; S l e a th , 1 9 7 6 ; A l le n , 1 9 7 9 ) a n d " p o s t - v o r t e x r i p p l e s " ( D i n gi e r, 1 9 7 4 ;D i n g i e r a n d I n m a n , 1 9 7 6 ) t o t h e v e r y s t ee p v a r ie t ie s t e r m e d ' v o r t e x r i p p le s '( B a g n o l d , 1 9 4 6 ; S l e a t h , 1 9 7 6 ) o r ' o r b i t a l r i p p l e s ' ( C l if t o n , 1 9 7 6 ) . T h e i d en -t i f i c a ti o n o f t h e s e r i p p l e t y p e s i n n a t u r a l e n v i r o n m e n t s h a s n o t a l w a y s b e e nu n e q u i v o c a l .T h e r e l a t io n s h i p b e t w e e n o r b i t a l d i a m e t e r o f w a t e r p a r t i c l e s a n d r i p p l es p a c i n g

M i ll er a n d K o m a r ( 1 9 8 0 a ) s u m m a r i z e d l a b o r a t o ry e x p e r i m e n t s s e ek i ngt o d e t e r m i n e t h e r e l a ti o n s h i p b e t w e e n n e a r -b e d o r b i ta l d i a m e t e r a n d ri p p le

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s p a c in g . O s c i ll a ti n g b e d s ( B a g n o l d , 1 9 4 6 ; M a n o h a r , 1 9 5 5 ; K a l k a n i s , 1 9 6 4 ;S l e a t h , 1 9 7 5 , 1 9 7 6 ) , o s c i ll a ti n g w a t e r t u n n e l s o r U - t u b e s ( C a r s t e n s e t a l. ,1 9 6 9 ; C h a n e t a l . , 1 9 7 2 ; M o g r i d g e , 1 9 7 3 ; B r e b n e r a n d R e i d e l , 1 9 7 3 ;L o f q u i s t , 1 9 7 7 , 1 9 7 8 ) a n d w a v e f l u m e s ( Y a l i n a n d R u s s e l l , 1 9 6 2 ; H o r i k a w aa n d W a t a n a b e , 1 9 6 7 ; M o g r id g e a n d K a m p h u i s , 1 9 7 3 ; D i n g l e r, 1 9 7 4 ; D i n g l e ra n d I n m a n , 1 9 7 7 ) h a v e b e e n u s e d t o s t u d y o s c i l l a t o r y f l o w s . F r o m t h e s ed a t a , f o r s m a ll o r b i ta l d i a m e t e r s , t h e r e l a t i o n s h i p b e t w e e n n e a r - b e d o r b i t a ld i a m ete r (d0) and r i pp l e spac ing (X) i s ve ry s imp le (F ig . l ) :

= 0 .65 do (1)( M i ll er a n d K o m a r , 1 9 8 0 , p . 1 7 8 ) , t h e f l u m e a n d U - t u b e d a t a p ro v i d i n g t h eb e s t f it t o t h is c u rv e . E q u a t i o n 1 ha s a w e a k R e y n o l d s n u m b e r d e p e n d e n c ed e m o n s t r a t e d i n d e p e n d e n t l y b y S l e a t h ( 1 9 7 6 ) a n d J a p a n e s e w o r k e r s ( e . g .H o m - M a e t a l. , 1 9 6 5 ) , b u t c a n b e n e g l e c t e d h e r e f o r s im p l i c i t y . A s n e a r -b e do r b i t a l d i a m e t e r i n c r e a s e s e q . 1 n o l o n g e r h o l d s , b e c o m i n g i n v a li d a s af u n c t i o n o f g r a i n siz e :~m~x = 0 .0 0 2 8 D 1"68 (2 )

O r b i t a l D i a m e t e r b a a e d o n H 1 / 3 ( m )0.1 1

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1 - 0 . 0 8 8 - 0 . 1 7 " / m m- i l l ~ n i 0 . 2 5 0 - 0 . 3 5 0 m m " ~ ' ~ ' - " ~ 5eo-710~Jm

0 . 5 0 0 - 0 . 7 1 0 m m, . q

E I n m e n 1 9 5 7 , D l n g l e r 1 9 7 4 ,' < M i l l e r a n d K o m a r 1 9 8 0 bo to

o - :( h e A " - . . . ? ~e ~ " " 25 0- 35 0p m

~t '0 .1 ~ e - -

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O r b i t a l D i a m e t e r b a s e d o n H r m s ( m )F i g .1 . R e l a t i o n s h i p b e t w e e n n e a r - b e d o r b i t a l d i a m e t e r o f w a t e r p a r t i c le s ( do ) a n d r i p p l es p a c i n g ( k ) w i t h d a t a s o u r c e s i n d i c a te d . N o t e t h e p o o r c o r r e l a t i o n b e t w e e n d o a n d k f o rd o a n d k > 0 . 2 m . H l l 3 i s s i g n i f ic a n t w a v e h e i g h t , H r m s is r o o t m e a n s q u a r e o f w a v eh e i g h t. M o d i f i e d f r o m M i l le r a n d K o m a r ( 1 9 8 0 b ) .

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458(Miller and Ko mar, 1980, p.180) where D is the median grain-diameter inmicrons and ~'max is in centime tres.

Allen (1979) showed th at ripple steepness is an impo rta nt fac tor influen-cing wave reconstructions. He plotted the data of Inman (1957), Kennedyand Falcon {1965), Manohar (1955), Inman and Bowen (1963), Hom-Maet al. (1965), Carstens et al. (1969), Lofquist {1978) and Sleath and Ellis(1978) on a dimensionless ripple spacing (k/D) versus dimensionless orbitaldiameter (do/D) diagram with ripple steepness as a further variable (Fig.2).A range of dimensionless orbital diameters could be obtained for a givenripple steepness. Equ ati on 1 then mer ely repre sented one limit on Allen'sfig.2 (1979, p.676) for vortex ripples, the other limit being determined forpost-vortex or rolling grain ripples (Sleath, 1975, 1976) as:0.036 < k/do < 0.059 (3)

I I I I I I I I I I I I 1 I I I 1 T I I I 1 I I . I . I

+ + ' Y, - ~ L o w - s t e e p n e s s r i p p l e s ~ . 5' +0 3m3=e . 1 2 " 5

0 5 ~ " 0 ' ~ 'c D ~ .E 1 0 2 b? ,

O ,Z , ' , & o / , b o /

I / / / /101 10 2 10 3 10 4

N o n - d i m e n s i o n a l o r b i t a l d i a m e t e r ( d o / D )Fig.2. Occurrence of wave ripple-marks as a function of dimensionless ripple spacing(k/D) and dimensionless near-bed orbital diameter of water particles (do/D). The lowerlimit of ripple occurrence is given by k/d o = 0.65 or 1,0 and the upper limits for givenripple steepnesses (vertical form indices) are given by the series of curves. Note that thecurves represent the upper limit of d o/D and are not isopleths. After Allen (1979, p.676).

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Allen (1981) suggested that the use of a wide range of ripple steepnessinevitably led to an unacceptably wide range of estimated orbital diameters,making wave reconstruct ions hazardous.The relationship between ripple spacing and grain and flow parameterscan be expressed as:= F(d0, v, D, Ps, P, g, ~) (4)

Since U o = c o d o / 2 , Sleath (1976) was able to express the relationship be-twee n orbital diame ter and ripple spacing for "rolling grain ripples" as a func-tion of four dimensionless variables:d o = F [[ 3D , R , p J p , (p~ - - p ) g D / p w v ] (5)2 ~where R = U o / (~ o v) 1 /2 is a form of wave Reynolds number and ~ = (o/2v) 1/2.It can be seen that three of these dimensionless groups contain w and onecontains U0. Only prior knowledge of U0 and an iterative solution of Sleath'sequations (1976, p. 78) would allow a solution to be made.Clearly, the best results will come from those ripple-marks for which anunambiguous relationship between orbital diameter and ripple spacing exists.Such vortex ripple-marks are defined by the incidence of flow separationover a steep crest. Bagnold (1946), J.F.A. Sleath (pets. commun., 1979)and Allen (1979) suggested limiting ripple steepnesses (expressed as a verticalform index, VFI; Bucher 1919) of 8.0, 8.3 and 7.5, respectively, and Dinglerand Inman (1977) stated an average value of 6.7 for vortex ripples. It isworth emphasising that ripple steepness is a function of several fluid, sedi-ment and flow-related variables but that ripple steepness alone is the pre-dominant control on the existence of vortex ripples. Extreme caution mustbe exercised in analysing low-steepness ripple-marks for wave reconstruc tionsand it is recommended that attention is focused on vortex ripple-markspossessing vertical form indices of less than 7.5 and certainly less than 10.T h e c r i t i c a l v e l o c i t i e s f o r w a v e r i p p l e f o r m a t i o n

The critical threshold for entrainment under waves is given by a modifiedShields parameter, and is determined by grain and fluid density (p,, p), fluidviscosity (~), grain diameter (D) and near-bed orbital diameter of waterparticles (do). For grain sizes of less than 0.5 ram, Komar and Miller's (1973)relation is:p V t 2 / ( p , - - p ) g D = 0.21 ( d o ~ D ) i n (6)which is based exclusively on Bagnold's (1946) data and corresponds tolaminar boundary layers. For grain sizes greater than 0.5 mm, Komar andMiller (1973) suggested the expression:p U t 2 / ( p 8 - - p ) g D "~ 0.46 ~ ( d o / D ) 114 (7)derived from the data of Rance and Warren (1969) which applies toturbulent boundary layers.

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R i p p l e s t e e p n e ss i s i n t i m a t e l y r e l a t ed t o p r o c e s s e s i n th e w a v e b o u n d a r yl a y e r. I t is t h e n e a r - b e d c u r v a t u r e - r e l a t e d d r i f t v e l o c i t i e s ( S l e a th , 1 9 7 5 ,1 9 7 6 ) w h i c h a r e d ir e c t ly r e s p o n s i b le f o r w a v e r ip p l e - m a r k f o r m a t i o n( B a g n o l d , 1 9 4 6 ; K a n e k o a n d H o n j i , 1 9 7 9 ) , w h e r e a s i t is t h e p u r e l y o s c i l-l a t o r y ( s im p l e h a r m o n i c ) c o m p o n e n t w h i c h ca u s e s m o s t g ra in m o v e m e n t .A l l e n ( 1 9 7 9 , f i g . l , p . 6 7 5 ) p l o t t e d t h e p u r e l y o s c i ll a to r y c o m p o n e n t , U reax,a g a i n st g r a in d i a m e t e r f o r a ra n g e o f s t e e p n e s s v a l u e s ( F i g .3 ) . T o g e t h e r w i t ht h e a n a ly s is o f K o m a r a n d M i l le r ( 1 9 7 6 ) , A l l en ' s c o m p i l a t i o n s h o w s t h a tw a v e r i p p l e - m a r k s o c c u r a t o r b i t a l v e l o c i t i e s w e l l a b o v e t h o s e a t t h e t h r e sh -o l d c o n d i t i o n , u p t o t h e p o i n t a t w h i c h r i p p le s ar e d e s t r o y e d a n d s h e e t f l o wc o m m e n c e s ( F i g. 3) .K o m a r a n d M i l l e r ( 1 9 7 6 ) g a v e t h e c r i t i c a l r e l a t iv e s t re s s f o r r i p p l e d i s a p -p e a r a n c e a s a f u n c t i o n o f g r a in s i ze a l o n e , a s :0 c = 0 . 41 3 D -'396 (8)

1.1

1 .o

0 -9io 0 . 8

EE 0 - 7

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o 0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1 .0 1 .1 1 - 2S e d i m e n t p a r t i c l e d i a m e t e r D ( r a m )

F i g .3 . O c c u r r e n c e o f w a v e r i p p l e - m a r k s a s a f u n c t i o n o f m a x i m u m n e a r - b e d o r b i t a lv e l o c i t y o f w a t e r p a r t i c l e s ( U m a x ) a n d g r a in s iz e o f s e d i m e n t ( D s 0 ) . T h e c u r v e s f o r r i p p l es t e e p n e s s ( v e r t i ca l f o r m i n d e x ) e n c l o s e t h e e x i s t e n c e - f i e l d o f r ip p l e - m a r k s w i t h a givens t e e p n e ss . A f t e r A l l e n ( 1 9 7 9 , p . 6 7 5 ) .

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o r in t e r m s o f gr ai n R e y n o l d s n u m b e r a s:0 c = 4 .4 0 (U ma xD /v) - '333 (9 )b o t h b a s ed o n M a n o h a r ' s ( 1 9 5 5 ) d a t a ( F ig . 4) . T h e s i m p l e r m e t h o d is t o g od i r e c t l y t o A l l e n ' s ( 1 9 7 9 ) f ig .1 w h i c h i s b a s e d o n a fa r w i d e r r a n g e o f d a t a.C a l c u l a ti o n o f w a v e p e r i o d

U s i n g l i n e a r w a v e t h e o r y , w h i c h i s a d e q u a t e f o r t h e s e p u r p o s e s ( L eM ~ h a u t ~ e t a l. , 1 9 6 9 ) , i t is p o s s ib l e t o r e l a t e n e a r - b o t t o m o r b i t a l d i a m e t e r sa n d v e l o c i ti e s t o w a v e p e r i o d ( T ) w i t h t h e s im p l e e x p r e s s i o n :Urea x = I rdo/T ( 1 0 )E q u a t i o n 1 0 i n d i c at e s t h a t a l t h o u g h t h e e n t i r e r a n g e o f c o n d i t i o n s f r o m th et h r e s h o l d v e l o c i t y t o t h e d e s t r u c t i o n v e l o c i t y s h o u l d b e s t u d i e d , i t i s t h et h r e sh o l d c o n d i t i o n ( m i n i m u m U 0) w h i c h g iv es t h e m a x i m u m w a v e p e r io d .M a x i m u m w a v e p e r i o d s a r e o f g r e a t e r i n t e r e s t i n r e c o n s t r u c t i n g a n c i e n t s e ac o n d i t io n s . I f o n e e x p e r i m e n t s w i t h t h e l im i t s o f th e r a n g e o f d o o b t a i n e da b o v e, a r an g e o f T f o r b o t h t h e t h r e s h o l d a n d d e s t r u c t i o n c o n d i t i o n iso b t a i n e d .T h e r a t i o n a l e b e h i n d c a l c u l a t i n g T i s t h a t t h e p e r i o d o f g r a v i t y w a v e s isd e t e r m i n e d b y w i n d s t r e n g th , d u r a t i o n a n d f e t c h . P l ac in g r e a s o n a b le l i m it so n w i n d s p e ed a n d d u r a t i o n ( f o r e x a m p l e , f o r ty p i c a l f a i r -w e a t h e r a n dt y p i c a l s t o r m c o n d i t i o n s ) , i t is p o s s ib l e t o u s e w a v e f o r e c a s t i n g m e t h o d s t od e r i v e f e t c h l im i t s f o r c a l c u l a t e d w a v e p e r i o d s ( S v e r d r u p a n d M u n k , 1 9 4 6 ;r e f i n e d b y B r e t s c h n e i d e r , 1 9 7 0 , o r D a r b y s h i r e a n d D r a p e r , 1 9 6 3 ) . I n f e t c h -l i m i t e d s e a s t h e a n a l y s is o f N e u m a n n ( 1 9 5 3 ) is p a r t i c u l a r l y u s e f u l ( F i g .5 ) .

l i l l i I I I I I I I I I I I I I I I I I I I , I I I l l i l | I I I i l , , l

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Fig. 4. Occurr ence of wave ripple- marks as a fun cti on of a Bagnold (1963)-Shields (1936)relative stress (O) and grain Reyn olds nu mbe r (Reg). The ripple existence-field was basedo n the laboratory data of Manohar (1955), Horikawa and Watanabe (1967) and Carstenset al. (1969) and the field data of Inman (1957). The bed planation threshold was con-structed from the data of Manohar (1955) and s upported by the theoretical criterion ofBagnold (1956, 1966). After Komar and Miller (1975, p.701).

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W A V E P E R I O D ( T ) s e cF i g . 5 . T h e e n e r g y d e n s i t y s p e c tr a f o r s e a c o n d i t i o n s w h e r e f e t c h i s l i m i t i n g , a ft e rN e u m a n n ( 1 9 5 3 ) .C a l c u l a t e d f e t c h e s f o r a n c i e n t w a v e s a r e a n im p o r t a n t a s se t in p a l a e o g e o -g r ap h ic al s t u d ie s . H o m e w o o d a n d A l le n ( 1 9 8 1 ) u s e d f e t c h le n g t h c a lc u l a te df r o m M i o c e n e w a v e r i p p le - m a r k s t o c o n f i r m t r a d i t i o n a l v i e w s , b a s e d o n t h ed i s t r i b u t i o n o f m a r i n e f a c ie s , o n t h e s iz e o f t h e p e r i- A l p in e s e a i n S w i t z e r l a n d .A l l e n ( 1 9 8 1 ) u s e d f e t c h d a t a t o p o s t u l a t e t h e e x t e n t o f a D e v o n i a n l ac u s-t r in e b as in w h e r e o u t c r o p s w e r e i n c o m p l e t e .S im u l a t i o n o f w a v el en g t h , w a v e h e i g h t an d w a t er d e p t h

T h e o r b i ta l d i a m e t e r o f w a t e r p a r t i cl e s n e a r t h e b e d is t h e r e s u l t o f a w a v eo f p e r i o d T , h e i g h t H a n d w a v e l e n g t h L a c t i n g in w a t e r d e p t h h . I t f o l l o w st h a t i t i s i m p o s s i b l e t o o b t a i n a u n i q u e s o l u t i o n t o H , L a n d h ; i t i s o n l yp o s s ib l e t o o b t a i n c o m b i n a t i o n s o f p a r a m e t e rs . T h i s is w h y e s t i m a t i o n o f H ,L a n d h is w e l l s u i t e d t o c o m p u t e r s i m u l a t i o n ( s e e K o m a r , 1 9 7 4 , f o r i n s t a n c e) .

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B e c a u s e d e e p - w a t e r w a v e s a re u n a f f e c t e d b y w a t e r d e p t h , i t is p o s s i b l e t oc o n s t r u c t d e e p - w a t e r w a v e l e n g t h b a s e d p u r e l y o n w a v e p e ri o d , a s f o l lo w s :L ~ = g T : / 2 ~ ( 1 1 )w h i c h is a si m p l i f i c a t i o n o f t h e g e n e r al c a s e :L = ( g T : / 2 ~ ) t a n h ( ~ ) ( 1 2 )

A s t h e w a v e tr a v e ls in t o s h a l l o w e r w a t e r i ts fo r m c h a n g e s s o t h a t o r b i t a ld i a m e t e r o f w a t e r p a r t ic l e s n e a r th e b o t t o m is g iv e n b y :d o = H / s i n h ( 2 n h / L ) ( 1 3 )I t is n e c e s s a r y th e r e f o r e t o s t u d y t h e t r a n s f o r m a t i o n s w h i c h t a k e p l a c e i na w a v e o f k n o w n p e r i o d T a s i t m o v e s i n t o s h a l l o w e r w a t e r . T h i s c a n b ed o n e i n v a r io u s w a y s , b u t a r e l a ti v e l y p a in l e s s m e t h o d is t o c a l c u l a t e h / L ~f o r t h e p r i m a r y f ie l d o f i n t e r e s t f o r w a t e r d e p t h a n d u s e t h e g r ap h s f o r A i r yw a v e t r a n s f o r m a t i o n s p r o v i d e d b y W i e ge l (1 9 6 4 ) ( Fi g. 6 ). A l t e rn a t i v e l y E c k a r t( 1 9 5 2 ) g a ve t h e a p p r o x i m a t i o n :L = L ~ a b s [ ta n h ( 2 ~ h / L ~ ) ] ( 1 4 )

T h e v a r i a t i o n o f H i s o f p a r t ic u l a r i n t e r e s t s in c e it a f f e c t s n e a r - b e d o r b i t a ld i a m e t e r . A s s u m i n g t h a t i n o r d e r t o f o r m t h e o b s e r v e d r ip p l e -m a r k s t h ew a v e s p o s s e s s e d f i n i t e n e a r - b o t t o m o r b i t a l d i a m e t e r s ( i . e . , t h e f o r m a t i v ew a v e s w e r e n o t d e e p - w a t e r w a v e s ), e q . 1 3 c a n b e u s e d t o o b t a i n w a v e h e i gh t .W a v e b r e a k i n g

T h e r e i s a n o t h e r l i m i t w h i c h i s c r it i ca l to t h e v a l i d i t y o f t h e r e c o n s t r u c t e dw a v e p a r a m e t e r s , t h a t o f w a v e b r e a k i n g . M i c h e (1 9 4 4 ) g i v es t h e l im i t i n gs t e e p n e s s f o r w a v e s in w a t e r o f f i n it e d e p t h a s:( H / L ) Hm = 0 . 1 4 2 t a n h ( 2 n h / L ) ( 1 5 )a n d i n p ro g r e s si v e l y s h a l lo w e r w a t e r ( M c C o w a n , 1 8 9 4 ) w a v e s b re a k a t:( H / h )n m = 0 . 7 8 ( 1 6 )E q u a t i o n 1 6 is s e n s it iv e t o b e a c h s l o p e ( I p p e n a n d K u l i n , 1 9 5 5 ) . F o r sm a l ls l o p e s ( t a n /3 < 0 . 0 7 ) :0 . 7 2 < ( H / h ) l i m < 1 . 1 8 ( 1 7 )a n d f o r a r e a s o n a b l e b e a c h s l o p e o f 0 . 0 0 3 :(H/h) l im = 0 , 8 8 ( 1 8 )w h i c h is i n c lo s e a g r e e m e n t w i t h e q . 1 6 . O n l y r a r e l y d o g e o l o g is t s h a v e d a t ao n a n c i e n t b e a c h s l o p e , so it is n o r m a l t o s i m p l y i m p l e m e n t e q s. 1 5 a n d 1 6 .

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irH / H m '~ !

i I

o .0 1 ~ - - ~ - ~ - ~0.001 0.01 0.1hLOO

Fig.6. The shoaling transformations for Air y waves as functions o f the rati o of waterdepth to deep-water wavelength, h /L= : . C , Cg and Coo are wave celerity (phase velocity),group velocity and deep-water celerity. H and H~o are wave height and deep-water waveheight. L and Loo are surface wavelength and deep-water wavelength, n is a shoaling coef-fici ent relat ing wave celerity to group velocity. Af ter Wiegel (1964).E n e r g y f l u x ( w a ve p o w e r )

T h e m o t i o n o f w a v e s p r o d u c e s a t r a n s fe r o f e n e r g y o v e r t h e s e a s u r fa c ew h i c h i s o f g r e a t i n t e r e s t t o p h y s i c a l o c e a n o g r a p h e r s a n d c o a s t a l e n g i n e e rs . Aw a v e t r a i n p o s se s se s a t o t a l e n e r g y m a d e u p o f t w o c o m p o n e n t s . T h e p o t e n -t ia l e n e r g y c o m p o n e n t is c a u s e d b y w a t e r p a r t ic l e s b e i n g d i s p l ac e d f r o m t h es ti ll w a t e r le v el , a n d t h e k i n e t ic e n e r g y c o m p o n e n t a c c o u n t s f o r th e o r b i t a lm o t i o n s o f w a t e r p a r t ic l e s . T h e t o t a l e n e r g y i s g i v en b y :E = pgI -P/8 ( 1 9 )( T e l ek i , 1 9 7 2 , p . 3 8 ; M a d s e n , 1 9 7 6 , p . 7 2 ) w h e r e E i s a s u r f a c e e n e r g y d e n -s it y p e r u n i t w i d t h o f w a v e c re s t. T h e r a t e a t w h i c h t h is e n e r g y i s p r o p a g a t e di n t h e d i r e c t i o n o f w a v e a d v a n c e i s t h e e n e r g y f l u x ( o r w a v e p o w e r ) , a n d isd i r e c t l y r e l a t e d t o t h e v e l o c i t y o f t h e w a v e tr a i n ( g r o u p v e l o c i t y C g ) r a t h e rt h a n t h e p h a s e v e l o c i t y o f i n d iv i d u al w a v e f o r m s . T h e e n e r g y f lu x p e r u n i tl e n g t h o f w a v e c r e s t is :

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P = pgH2 CJ8 (20)Group velocity can be obtained from Wiegel's {1964) Airy wave transforma-tions as the dimensionless ratio Cg/C (Fig. 6) by use of the expression forwave phase velocity (celerity):C = L/ T = (gT/2~) tanh (2~h/L) (21)where C = Coo = gT/27r in deep water.Energy flux for reconstructed wave conditions should decrease in shal-lowing waters, the ratio of deep-water energy flux to shallow-water energyflux providing an index of power attenuation. Homewood and Allen (1981)used estimates of energy flux to provide modern analogues to the MioceneSea of Switzerland by comparison with the energy flux (wave power) da ta ofColeman and Wright (1975) and Wright and Coleman (1973).THE UPPER MARINE MOLASSE OF SWITZERLAND

The wedge of Tertiary clastic sediments north of the Swiss Alps is tradi-tionaUy subdivided into four units (Matter et al., 1980; and Fig.7A). Thelowermost, of Oligocene age, is termed the Lower Marine Molasse andrepresents offshore mudstones with storm sandstones and culminates in awave-dominated shoreline sequence. The overlying unit, the Lower Fresh-water Molasse comprises predominantly fluviatile clastic sediments withsome playa and lacustrine sediments. The third unit is the Upper MarineMolasse of Miocene (Burdigalian) age, consisting of wave- and tide-dominatedshallow mar ine sandstones and the conglomerates of fringing fan-deltas. Theuppermost unit, the Upper Freshwater Molasse is composed of alluvial fanand fluviatile clastics and lacustrine deposits.The Upper Marine Molasse was deposited in a peri-Alpine depression nor thof the Alps (Fig.7B) which ex tended eastward to the Austro-Vienna basinand southwestward into France. Although wave-formed structures occurthroughout the Upper Marine Molasse, the present study concerns the areain the vicinity of Fribourg where road cuttings and river gorges providespectacular sections through the marine sand bodies.In the Fribourg area Homewood {1978, 1981) described four facies beltsin the Upper Marine Molasse (Fig.7C). The proximal facies belt, restrictedto the south (Hoffman, 1960), is composed of thick fan-delta deposits whichrepresent the major feeder systems of sediments from the Alpine hills to themarine seaway. A coastal facies belt contains abundant tidal sandwaves(Allen and Homewood, 1984) interbedded with intertidal sandflat depositsand distributary and tidal channel sandstones. The nearshore facies belt iscons truc ted of thick, elongate subtidal shoals with shoal crevasse deltas andintershoal swales. The offshore facies belt contains sandy and pebblycoquinas deposited as giant-sized flow-transverse tidal bedforms.

Wave ripple-marks are very common in the coastal, nearshore and off-shore facies belts. Homewood and Allen (1981, pp.2540- -2543) summarized

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- ~ ~, A

. " I " Z I M O L A S S E = o o =

I / /.-" I F ~O 0 i % I ~ ' 1 \ )" J ~ , , I w MOLASSE

, WTHD~T~~U:::LYu CE SHOALS 'I

/ C O A S T A L S A N D F L A T S ~ C O Q U I N A , , , N K S /

Fig.7. A. The f our l ithostr atigraphic subdiv isions of the Swiss Molasse after Mat ter et al.(1980). B. Palaeogeographic map of the Upper Marine Molasse of Switzerland with loca-tion of major fan-deltas, after Hofmann (1960), Rigassi, in Matter et al. (1980) andLemcke (1981). F marks city of Fribourg. C. Diagrammatic recon stru ctio n of distri butio nof facies belts in the Fribourg area during Burdigalian (Miocene) times (not to scale).G I = Gibloux fan; G U = Guggisberg fan; T B = transverse bars in tidally influenced dis-tributaries; T S = tidal sandwaves in coastal be lt; S = elonga te subtidal shoals in nearshorebelt; C = coquina banks in offshore belt. After Homew ood and Allen (1981).t h e m a j o r f i nd i n g s o f a s t u d y o f an c i e n t w a v e a n d t i d e c o n d i t i o n s f r o m t h e s ef a c i e s b e l t s .R e c o n s t r u c t e d s ea c o n d i t i o n s

T h e w a v e r i p p l e - m a r k s m e a s u r e d i n th e f i e ld p o s se s s t h e s y m m e t r i e s a n ds t e e p n e s se s s h o w n i n F i g .8 . C a r e w a s t a k e n t o o m i t r i p p le - m a r k s w h i c h w e r eo f q u e s t i o n a b l e o r ig in , i n p a rt i c u la r t h o s e re s u lt in g f r o m p r o b a b l e c o m b i n e df l o w s o f w a v e s s u p e r i m p o s e d o n ti d a l c u r r e n ts . S u c h r i p p l e -m a r k s w e r es o m e w h a t m o r e a s y m m e t r i c a n d w e r e c o m m o n l y a s so c i at e d w i t h t h e f la n k so f t i d a l s a n d w a v e s . A l a rg e n u m b e r o f r i p p l e - m a r k s h a v e s t e e p n e s s e s ( la r geV F I ) t h a t m a k e e s t im a t i o n o f a n c i e n t w a v e c o n d i t i o n s h a z a r d o u s b e c a u s e o ft h e w i d e r a n g e o f p o s s i b l e o r b i ta l d i a m e t e r s . F i f t y - t h r e e o u t o f 1 5 0 ri p p le -

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n i i i , I i i n i i i J i i i0. 5 , e, ) .

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m ~ 0 - 4 " " ~ ~ " " Ik d O ' . % ;x 0.3I I M z 0 . 2

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Fig.8. Plot of an index of s ymmet ry against ripple steepness (vertical form index) forwave ripple-marks from the Upper Marine Molasse near Fribourg. After Homewood andAllen (1981).m a r k s a r e c l ea r ly o f t h e v o r t e x t y p e , w h e r e e q . 1 c a n b e u s e d w i t h c o n f i-d e n c e , a n d o n l y t h r e e o f t h e s e 5 3 r i p p l e -m a r k s h a d a s p a c in g g r e a t e r t h a n)kmax i n e q . 2 ( F i g . 9 ) . B e a r i n g i n m i n d t h e o r i g i n al s c a t t e r o f d a t a f r o m e q . 1a n d d i f f i c u l t i e s o f a c c u r a t e f i e ld m e a s u r e m e n t s , i t i s j u s t i f i a b l e t o s i m p l y u s et h e t h r e s h o l d c o n d i t i o n f o r v o r t e x r i p p le s i n e s t i m a t i n g w a v e p e r i o d f r o mo r b i t al d i a m e t e r a n d o r b i t a l v e l o c i t y ( F i g .1 0 ) .

F o r e a c h l o c a l i t y a t a b l e w a s c o n s t r u c t e d g i vi n g l e n g t h s a n d h e i g h t s o ff o r m a t i v e w a v e s o v e r a r a n ge o f w a t e r d e p t h s . U n r e a s o n a b l e c o m b i n a t i o n so f H , L a n d h w e r e t h e n e l i m i n a t e d a c c o r d i n g t o w a v e b r e a k i n g c r i t e ri a . I nt hi s w a y , a n i m p r e ss io n o f th e m a x i m u m w a t e r d e p t h s at w h i c h th e w a v er i p p le - m a r k s f o r m e d w a s o b t a i n e d . A n e x a m p l e f o r o n e l o c a l it y is g iv e n i nT a b l e I .

W a t e r d e p t h s u n d e r f o r m a t i v e w a v e s w e r e in m o s t c a s es le ss t h a n 2 5 m ,b u t i n e x t r e m e c a se s v e r y h ig h w a v e s n e a r t h e b r e a k i n g l i m i t m a y t h e o r e t i-c a l ly h a v e b e e n r e s p o n s i b l e f o r t h e w a v e r i p p le - m a r k s i n d e e p e r w a t e r s ,p e r h a p s u p t o 6 0 m . S u c h l ar g e w a t e r d e p t h s a re u n l i k e l y f r o m t h e fa c ie sa s so c i at io n s . F u r t h e r m o r e , t h e a s s o c i a ti o n o f w a v e r i p p le - m a r k s w i t h t i d als a n d w a v e s s h o w i n g s h a l l o w - s t a g e r u n - o f f p a t t e r n s a n d m i n i r i p p l e s (a s a tI ll en s , m a p c o - o r d . 5 7 4 . 5 0 / 1 7 6 . 5 0 , S w i ss t o p o g r a p h i c m a p s N o . 2 5 2 ) a n d

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0 1 0"2 0"3 0'4D ( m m )

F i g .9 . P l o t o f m e d i a n g r a i n s i z e a g a i n s t r i p p l e s p a c i n g s h o w i n g t h e r i p p l e s p a c i n g a t w h i c ht h e l i n e a r r e l a t i o n s h i p b e t w e e n o r b i t a l d i a m e t e r a n d r i p p l e s p a c i n g ( e q . 1 ) b r e a k s d o w n( d a s h e d l i n e ) . D o u b l e b l a c k c i rc le s, o r t e x r i p pl e s, F I < 7 . 5 , d o u b l e o p e n c ir cl es , o r t e xr i p pl e s w i t h ~ > ~ m a x ; s m a l l d o t s , l o w - s te e p n e s s r i pp l es , F I > 7 . 5 . N u m b e r o f s u p e r i m -p o s e d d a t a p o i n t s a l s o i n d i c a t e d f o r v o r t e x r i p p le s .

s w a s h b a r s o r fl o od r a m p s (as a t F r ib o ur g , 5 7 8 . 9 0 / 1 8 4 . 7 0 M a p 2 4 2 ) s u gg e st st ha t w a t e r d e p t h s w e r e s ha ll ow , a n d m o s t w a v e r ip pl e- ma rk s m a y h a v e b e e np r o d u c e d u n d e r m o d e s t f a ir - we a th e r w a ve s .

T h e variability of reconstructed wa ve conditions b et we en localities isno t great, bu t it m a y be explained by the relative exp osu re or sheltering ofs u b - e n v i r o n m e n t s f r o m w a v e a t t a c k a n d t o t h e v is ci ss it ud es o f d e p t h d u r i n gthe tidal cycle. In the cas e of the offshore facies comp risi ng co qu in a banks,t h e r e c o n s t r uc t e d w a v e p e r i od s a r e g e n e ra l l y a b o u t 3 s a n d w a t e r d e p t h sm u s t h a v e b e e n l e ss t h a n 1 0 m f o r f o r m at i v e w a v e s . S i nc e t he s e r i p p le - m a rk soriginate fr om the facies m o s t distal fr om the shoreline in the sou th, it isi n c o nc e i v ab l e t h a t m o r e p r o x i m a l f a c i es w e r e d e p o si t e d i n w a t e r d e p t h s

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469

COA STA L' t NEARSHORE ' ~OFFSHORE t

10 . . . .

I I

o [ " - - J I I =1 2 3 4 5 6 7 2 3 4 5 6 7 1 2 3 4T (sec s) T (secs ) T (see s)

IO0TOTAL >.UI "

Eu.wI -,~ gO.1

I-ZwKw

I I L2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

T (s ee s) T (SeCS)Fig.10. Histograms of calculated max imu m wave periods o f formative waves for thecoastal, nearshore and offshore facies belts and histogram and cumulative frequ encycurve for total. Assumes the threshold cond itio n and eq.1, utilizing vort ex ripple-markdata only.TABLE IExampl e o f work-sheet for each locality showing wave transfo rmatio ns in shallowingwater depths. Asterisk at h = 20 m indicates unstable wave conditions. Terms definedin text and caption to Fig.6; h, L and H are in metresWater ( h / L o ~ ) ( L / L o o ) ( H / H o ~ ) Shoaling (Cg/C~o) Surface Surface wavedepth coeffic ient wavelength height(h) (n) (L) (H)

0.5 0.019 0.33 1.30 0.97 0.33 8.58 0.061.0 0.038 0.48 1.10 0.93 0.42 12.48 0.085.0 0.192 0.85 0.91 0.68 0.59 22.10 0.3110.0 0.385 0.99 0.99 0.53 0.53 25.74 0.9120.0 0.769 1.00 1.00 0.50 0.50 26.00 9.8*Locality: Cbtes vers le Lac, Estavayer -- Yverdon Road. Mean of maximum wave periods:4.08 s. Deep-water wave length: 26.0 m.

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470substantially greater than this. The apparent landward increase in period offormative waves (Fig.10) may be due to a steadily increasing fetch for thenortherly or westerly winds, as the Jura coast became more distant and theAlpine shore was approached.

The calculated values of wave power (or energy flux) fall within a widerange of appr oxim ate ly 10s--106 erg s-'. It mu st be stressed that calculatedwave power values are highly sensitive to estimated water depth since hdetermines the height of formative waves. Nevertheless, bearing in mindthe probable errors, it is possible to compare the wave power at the coastof the Burdigalian Sea in the Fribourg area to that of the Danube, Ebro,Niger and Nile deltas (Table II; Coleman and Wright, 1975). In contrast,the wave -dom inat ed deltas such as the S~o Franci sco and Senegal aremoulded by considerably more powerful waves than those estimated forthe Burdigalian Sea. Delta m orp hol ogy is also a func tio n of river input(discharge effectiveness index) and tidal range. H om ew ood and Allen's{1981) pl ots using wave pow er, discharge effe ctive ness inde x and tidal rangeas the three controlling parameters suggested that the closest affinities of theBurdigalian coastal systems in the Fribourg area lie with the present-daydeltas of the Niger and possibly Burde kin and Klang.Comparing the wave power calculated for the offshore coquina bankfacies to that of the coastal swash bar or flood ramp facies, representing thepassage from the open Burdigalian seaway to the Alpine coast, there appearsto have been a wave attenuation of between 50:1 and 100:1.

CONCLUSIONSFurther case-studies of wave-influenced sedimentary sequences are re-

quired to broaden the presently inadequate data base. Substantial progressTABLE IIYear-average wave powers for seven of the world's major deltas and estimated values forthe BurdigalianSea of western Switzerland (Fribourg area). Wright and Coleman's (1973)data have been converted to metric c.g.s, units. The Fribourg molasse values are derivedfrom formative waves in 10 m water depth and in depths of less than 2 m for shorelinewave powersD e l t a Y e a r - a v e r ag e w a v e Y e a r - a v e r a g e wavep o w e r a t 1 0 m c o n t o u r p o w e r a t shorelineergs-~ X 10 7 ergs -~ 10 7M i s s i s s i p p i 1 9 0 0 . 0 4 1Danube 49 0.037Ebro 172 0.155Niger 107 2.01Nile 128 10.17S~o Francisco 598 30.37Senegal 285 114.72Fribourg Molasse 10--50 0.1--1.0

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4 7 1

i n t h e q u a n t i f i c a t i o n o f a n c ie n t w a v e c o n d i t i o n s c a n o n l y b e m a d e p o s s i b l eb y a d v a n c e s i n o u r k n o w l e d g e o f t h e r e l a ti o n s h i p b e t w e e n n e a r - b e d o r b i t a ld i a m e t e r o f w a t e r p a r t i c l e s a n d r i p p l e - m a r k s p a c in g . I n th i s re s p e c t , l i n k a g eo f c h a r a c t er i s ti c r ip p l e g e o m e t r y o r in t e rn a l s t r u c t u r e w i t h f l o w p a r a m e t e r si s n e c e s s a r y .

T h e r e c o n s t r u c t e d s e a c o n d i t i o n s o f t h e M i o c e n e ( B u r d i ga l ia n ) S e a i n t h eF r i b o u r g a r e a o f w e s t e r n S w i t z e r l a n d a r e o f m o d e r a t e p e r i o d w a v e s ( 3 - - 6 s).F e t c h l e n g th s f o r s u c h w a v e s w e r e o f th e o r d e r o f 1 0 0 k m , p l a c in g s o m ec o n s t r a i n t o n t h e m i n i m u m s iz e o f t h e s e a w a y . T h e e s t i m a t e d w a v e p o w e ro f t h e B u r d i g a li a n S e a i n d i c a t e s a n a f f i n i t y w i t h s e a c o n d i t i o n s o f f d e l t a ss u c h a s t h e E b r o a n d D a n u b e , l o c a t e d in s e m i - r e s t r ic t e d s e as , b u t t i d al ra n g ew a s s u b s t a n t i a l l y l a rg e r t h a n i n t h e s e t w o e x a m p l e s .A C K N O W L E D G E M E N T S

I a m g r a t ef u l t o J o h n A l l en , P e t e r H o m e w o o d a nd D a r w i n S p ea r in g f o rt h e ir u s e f u l c o m m e n t s o n t h e m a n u s c r i p t . D a t a w e r e c o l le c t e d w i t h th ef in a n c ia l s u p p o r t o f t h e S w i ss N a t i o n a l S c i e n c e F o u n d a t i o n , P r o j e c t 2 . 2 4 2 -0 . 7 9 .R E F E R E N C E SA l l e n , G . P ., L a u r i e r , D . a n d T h o u v e n i n , J . , 1 97 9 . E t u d e S ~ d i m e n t o l o g i q u e d u D e l t a d uM a h a k a m . N o t e s e t M ~ m o i r e s N o . 1 5 , C o m p a g n i e F r a n ~ a i s e d e s P ~ tr o l e s, P a ri s.A l l e n , J . R . L . , 1 9 7 9 . A m o d e l f o r t h e i n t e r p r e t a t i o n o f w a v e ri p p l e - m a r k s u s in g th e i r

w a v e l e n g t h , t e x t u r a l c o m p o s i t i o n a n d s h a p e . J . G e o l . S o c . L o n d o n , 1 3 6 : 6 7 3 - - 6 8 2 .A l l e n , P . A . , 1 9 8 1 a . W a v e - g e n e r a t ed st r u c t u r e s i n th e D e v o n i a n l a c u s t r i n e s e d i m e n t s o fS E S h e t l a n d , a n d a n c i e n t w a v e c o n d i t i o n s . S e d i m e n t o l o g y , 2 8 : 3 6 9 - - 3 7 9 .A l l e n , P . A . , 1 9 8 1 b . S o m e g u i d e l i n e s i n r e c o n s t r u c t i n g a n c i e n t s e a c o n d i t i o n s f r o m w a v er i p p l e m a r k s . M a r. G e o l . , 4 3 : M 5 9 - - M 6 7 .A l l e n , P . A . a n d H o m e w o o d , P . , 1 9 8 3 . M e c h a n i c s a n d e v o l u t i o n o f a M i o c e n e t i d a l s a n d -w a v e. S e d i m e n t o l o g y , 3 1 : 6 3 - - 8 2 .B a g n o l d , R . A . , 1 9 4 6 . M o t i o n o f w a v e s i n sh a l l o w w a t e r . I n t e r a c t i o n s b e t w e e n w a v e s a n ds a n d b o t t o m s . P r o c . R . S o c . L o n d o n , S e r . A , 1 8 7 : 1 - - 1 5 .B o e r s m a , J . R . , 1 9 7 0 . D i s t i n g u is h i n g fe a t u r e s o f w a v e - r i p p l e c r o s s - s t r a t i f ic a t i o n a n dm o r p h o l o g y . P h . D . T h e s is , U n i v e r s it y o f U t r e c h t , U t r e c h t , 6 5 p p . ( u n p u b l . ) .B r e b n e r , A . a n d R e i d e l , P .H . , 1 9 7 3 . A n e w o s c i l la t i n g w a t e r t u n n e l . J . H y d r a u l . R e s . ,1 1 : 1 0 7 - - 1 2 1 .B r e t s c h n e i d e r , C . L . , 1 9 6 6 . W a v e g e n e r a t i o n b y w i n d , d e e p a n d s h a l l o w w a t e r . I n : A . T .I p p e n ( E d i t o r ) , E s t u a r y a n d C o a s t l in e H y d r o d y n a m i c s . M c G r a w H i ll , N e w Y o r k , N . Y .,p p . 1 3 3 - - 1 9 6 .B u c h e r , W . H . , 1 9 1 9 . O n r i p p l e s a n d r e l a t e d s e d i m e n t a r y s u r f a c e f o r m s a n d t h e i r p a l a e o -g e o g r a p h i c i n t e r p r e t a t i o n s . A m . J . S ci ., 4 7 : 1 4 9 - - 2 1 0 , 2 4 1 - - 2 6 9 .C a r s t en s , M . R . , N i e ls o n , F . M . a n d A l t i n b i l e k , H . D . , 1 9 6 9 . B e d f o r m s g e n e r a t e d i n t h el a b o r a t o r y u n d e r a n o s c i l la t o r y f l o w : a n a l y t i c a l a n d e x p e r i m e n t a l s t u d y . U .S . A r m yC o a s t a l E n g. R e s . C e n t r e , T e c h . M e m o . 2 8 .

C h a n , K . W . , B a i rd , M . H . I . a n d R o u n d , G . F . , 1 9 7 2 . B e h a v i o u r o f b e d s o f d e n s e p a r t i c l e si n a h o r i z o n t a l l y o s c i l l a t i n g l i q u i d . P r o c . R . S o c . L o n d o n , S e r. A , 3 3 0 : 5 3 7 - - 5 5 9 .C l i ft o n , H .E . , 1 9 7 6 . W a v e - fo r m e d se d i m e n t a r y s t r u c t u r e s - - a c o n c e p t u a l m o d e l . I n :R . A . D a v ie s a n d R . L . E t h i n g t o n ( E d i t o r s ) , B e a ch a n d N e a r s h o r e S e d i m e n t a t i o n . S o c .E c o n . P a l e o n t o l . M i n e r a l . , S p e c . P u b l ., 2 4 : 1 2 6 - - 1 4 8 .

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472

Coleman, J.M. and Wright, L.D., 1975. Modern river deltas: variabi lity of processes andsand bodies. In: M.L. Broussard (Editor), Deltas, Models for Exploration. HoustonGeol. Soc., pp.99--149.Cook, D.O. and Gorsline, D.S., 1972. Field observations of sand tra nsport by shoalingwaves. Mar. Geol., 13: 31--56.Darbyshire, M. and Draper, L., 1963. Forecasting wind-generated sea waves. Engineering(London), 195: 482--484.Dingler, J.R., 1974. Wave-formed ripples in nearshore sands. Ph.D. Thesis, Univ. ofCalifornia, San Diego, Calif., 136 pp.Dingler, J.R., 1979. The threshold of grain mot ion und er oscillatory flow in a laborato rywave channel. J. Sediment. Petrol., 49: 2 87 -2 94 .Dingler, J.R. and Inman, D.L., 1977. Wave-formed ripples in nearshore sands. Proc.15th Conf. Coastal Engineering, pp.2109- -2126.Eckart, C., 1952. The propagation of gravity waves from deep to shallow water. U.S.Nat. Bur. Stand. Gravity Waves, Circ., 521: 165--173.Harms, J.C., 1969. Hydraulic significance of some sand ripples. Geol. Soc. Am. Bull.,80: 363--396.Hoffman, F., 1960. Materialherkunft, Transp ort und S edimen tatio n im SchweizerischenMolassebecken. Jahrb. St. Gallischen Naturwissensch. Ges., 76: 5--28.Hom-Ma, N., Horikawa, K. and Hajima, R., 1965. A study on suspended sediment due towave action. Coastal Eng. Jpn., 8: 85--103.Homewood, P., 1978. Exemples de s~quences de facies dans la molasse fribourgeoise etleur interpretation. Soc. Fribourg Sci. Nat. Bull., 67 : 73--82.Homewood, P., 1981. Facies et enviro nnem ents de depbt de la Molasse de Fribourg.Eclogae. Geol. Helv., 74: 29--36.Homewood, P. and Allen, P.A., 1981. Wave-, tide- and curr ent- cont rol led sandb odies ofMiocene Molasse, western Switzerland. Bull. Am. Assoc. Pet. Geol., 65: 2534- 2545.Horikawa, K. and Watanabe, A., 1967. A study of sand movement due to wave action.Coastal Eng. Jpn., 10: 39--57.Inman, D.L., 1957. Wave generated ripples in nearshore sands. U.S. Technoh Memo.Beach Erosion Board, 100, 42 pp.Inman, D.L. and Bowen, A.J., 1963. Flume experiments on sand transport by waves andcurrents. Proc. 8th Conf. Coastal Engineering, 1: 137--150.Ippen, A.T. and Kulin, G., 1955. The shoaling and breaking of the solitary wave. Proc.5th Conf. Coastal Engin eering, pp.27--49.Kalkanis, G., 1964. Tran spor tatio n of bed material due to wave action. U.S. Army CorpsEngrs, Coastal Eng. Res. Centre, Tech. Memo., 2, 38 pp.Kaneko, A. and Honji, H., 1979. Initi ation of ripple marks un der oscillating water.Sedimentology, 26: 101--113.Kennedy, J.F. and Falcon, M., 1965. Wave generated sediment ripples. M.I.T. Dept. Civ.Eng. Hydro. Lab. Rept. 86, 55 pp.Komar , P.D., 1974. Oscillatory ripple marks and the evaluation of ancien t wave condi-tions and environmen ts. J. Sediment. Petrol., 44: 169--180.Komar, P.D., 1976. Beach Processes and Sedi ment atio n. Prentice-Hall, Englewood Cliffs,

N.J., 429 pp.Komar, P.D. and Miller, M.C., 1973. The threshold of sediment movement under oscil-latory water waves. J. Sediment. Petrol., 43: 110 1--1 110.Komar, P.D. and Miller, M.C., 1976. The ini tia tion of oscillatory ripple marks and thedevelopment of plane-bed at high shear stresses under waves. J. Sediment. Petrol.,45: 697--703.Le M6haut~, B., Divoky, D. and Lin, A., 1969. Shallow water waves: a comparison oftheories and experiments. Am. Soc. Civ. Eng., Proc. 11th Conf. Coastal Engineering,pp.86--96.

Lofquist, K.E.B., 1977. A positive displacement oscillatory water tunnel. Coastal Eng.Res. Centre, Misc. Rep., 77-1, 26 pp.

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4 7 3L o f q u i s t , K . E . B . , 1 9 7 8 . S a n d r i p p l e g r o w t h i n a n o s c i l l a t o r y - f l o w w a t e r t u n n e l . T e c h .P a p . U . S . C o a s t a l E n g . R e s . C e n t r e , 7 8 - 5 , 1 0 1 p p .M a d s e n , O . S ., 1 9 7 4 . W a v e c l im a t e o f t h e c o n t i n e n t a l m a r g i n ( i t s m a t h e m a t i c a l d e s c r ip -t i o n ) . I n : D . J. S t a n l e y a n d D . J . P . S w i f t ( E d i t o r s ) , T h e N e w C o n c e p t s o f C o n t i n e n t a lM a r gi n S e d i m e n t a t i o n - - S e d i m e n t T r a n s p o r t a n d i t s A p p l i c a t i o n t o E n v i ro n m e n t a lM a n a g e m e n t . S h o r t C o u r s e L e c t u r e N o t e s , A m . G e o l . In s t. , p p . 4 2 - -1 0 8 .M a n o h a r , M . , 19 5 5 . M e c h a n i c s o f b o t t o m s e d i m e n t m o v e m e n t d u e t o w a v e a c t i on . U . S .A r m y C o r p s E n g r s, B e a c h E r o s i o n B d . , T e c h . M e m o . , 7 5 , 1 2 1 p p .M a t t e r , A . e t a l ., 1 9 8 0 . F l y s c h a n d M o l a s se o f c e n t r a l a n d w e s t e r n S w i t z e r l a n d . In "R . T r u m p y ( E d i t o r ), G e o l o g y o f S w i t z e r la n d , a G u i d e B o o k . E x c . 1 2 6 A , 2 6 t h I n t .G e o l . C o n g r es s , P a r i s , S c h w e i z . G e o l . K o m m . , p p . 2 6 1 - - 2 9 3 .M c C o w a n , J . , 1 8 9 4 . O n t h e h i g h e s t w a v e o f p e r m a n e n t t y p e . P h i lo s . M a g . , 5 : 3 5 1 - - 3 5 7 .M i c h e , R . , 1 9 4 4 . U n d u l a t o r y m o v e m e n t s o f th e s e a i n c o n s t a n t a n d d e c r e a s i n g d e p t h .A n n . P o n t s C h a us s, M a y - - J u n e , J u l y - - A u g u s t , 2 5 - - 7 8 , 1 3 1 - - 1 6 4 , 2 7 0 - - 2 9 2 ,3 6 9 - - 4 0 6 .M i l le r , M . C . a n d K o m a r , P . D . , 1 9 8 0 a . O s c i l l a t i o n s a n d r i p p l e s g e n e r a t e d b y l a b o r a t o r ya p p a r a t u s . J . S e d i m e n t . P e t r o l . , 5 0 : 1 7 3 - - 1 8 2 .M i l le r , M .C . a n d K o m a r , P . D . , 1 9 8 0 b , A f i e ld in v e s t i g a t i o n o f t h e r e l a t io n s h i p b e t w e e n

o s c i l l a t i o n r i p p l e s p a c i n g a n d t h e n e a r - b o t t o m o r b i t a l m o t i o n s . J. S e d i m e n t . P e t r o l . ,5 0 : 1 8 3 - - 1 9 1 .M o g r i d g e , G . R . , 1 9 7 3 . B e d f o r m s g e n e r a t e d b y w a v e a c t i o n . D M E / N A E Q . B u l l ., 1 9 7 3 ( 2 ) ,4 1 p p .M o g r i dg e , G . R . a n d K a m p h u i s , J . W . , 1 9 7 3 . E x p e r i m e n t s o n b e d f o r m g e n e r a t i o n b y w a v ea c t i o n . A m . S o c . C iv . E n g r . , P r o c . 1 3 t h C o n f . C o a s t a l E n g i n e e r i n g , p p . 1 1 2 3 - - 1 1 4 2 .N e u m a n n , G . , 1 9 5 3 . O n o c e a n w a v e s p e c t r a a n d a n e w w a y o f fo r e c a s t in g w i n d - g e n e r a t e ds ea . U .S . A r m y C o r p s E n g . , B e a c h E r o s i o n B o a r d , T e c h . M e m . , 4 3 , 42 p p .N e w t o n , R . S . , 1 9 6 8 . I n t e r n a l s tr u c t u r e o f w a v e - f o r m e d ri p p l e m a r k s i n t h e n e a r s h o r ez o n e . S e d i m e n t o l o g y , 1 1 : 2 7 5 - - 2 9 2 .R a n c e , P . J. a n d W a r r e n , N . F . , 1 9 6 9 . T h e t h r e s h o l d o f m o v e m e n t o f c o a r s e m a t e r i a l i no s c i l l a t o r y fl o w . A m . S o c . C i v . E n g . , P r o c . l l t h C o n f . C o a s t a l E n g i n e e r i n g ,p p . 4 8 7 - - 4 9 1 .R e i n e c k , H . E . , S i n g h , I. B . a n d W u n d e r l i c h , F . , 1 9 7 1 . E i n t e i l u n g d e r R i p p e l n u n d a n d e r e rm a r i n e r S a n d k o r p e r . S e n c k e n b e r g i a n a M a r it . , 3 : 9 3 - - 1 0 1 .S l e a t h , J . F . A . , 1 9 7 5 . A c o n t r i b u t i o n t o t h e s t u d y o f v o r t e x r ip p l e s . J . H y d r a u l . R e s . ,1 3 : 3 1 5 - - 3 2 8 .S l e a t h , J .F . A . , 1 9 7 6 . O n r o l l i n g g r a in r ip p l e s . J . H y d r a u l . R e s . , 1 4 : 6 9 - - 8 0 .S l e a t h , J . F . A . a n d E l li s, A . C . , 1 9 7 8 . R i p p l e g e o m e t r y i n o s c i l l a t o r y f l o w . U n i v.C a m b r i d g e D e p t . E n g r . R e p t . A / H y d r a u l i c s ] T R 2 , 1 5 p p .S t o n e , R . O . a n d S u m m e r s , H . J . , 1 9 72 . S t u d y o f s u b a q u e o u s a n d s u b a e r i a l s a n d r i p p l e s.U n i v . S . C a l i f . D e p t . G e o l . S c i . , F i n a l R e p t . , 7 2 - 1 .S v e r d r u p , H . U . a n d M u n k , W . J. , 1 9 4 6 . E m p i r i c a l a n d t h e o r e t i c a l r e l a t i o n s b e t w e e n w i n d ,s e a a n d s w e l l. E O S , T r a n s . A m . G e o p h y s . U n i o n , 2 8 : 8 2 3 - - 9 2 7 .T a n n e r , W . F . , 1 9 6 7 . R i p p l e m a r k i n d i c e s a n d t h e i r us e s. S e d i m e n t o l o g y , 9 : 8 9 - - 1 0 4 .T a n n e r , W . F . , 1 9 7 1 . N u m e r i c a l e s t i m a t e s o f a n c i e n t w a v e s, w a t e r d e p t h a n d f e t c h . S e d i -m e n t o l o g y , 1 6 : 7 1 - - 8 8.T e l e k i , P . G . , 1 9 7 2 . W a v e b o u n d a r y l a y e r s an d t h e i r r e l a t i o n t o s e d i m e n t t ra n s p o r t . I n :D . J .P . S w i f t , D .B . D u a n e a n d O . H . P i l k e y ( E d i t o r s ) , S h e l f S e d i m e n t T r a n s p o r t : P r o c e s sa n d P a t t e r n . D o w d e n , H u t c h i n s o n a n d R o s s, S t r o u d s b o u r g , P a ., p p . 2 1 - -6 0 .W i e g e l, R . L . , 1 9 6 4 . O c e a n o g r a p h i c a l E n g i n e e ri n g . P r e n t i c e H a ll , E n g l e w o o d C l i f fs , N . J . ,5 3 2 p p .W r i g h t , L .D . a n d C o l e m a n , J . M . , 1 9 7 3 . V a r i a t i o n s i n m o r p h o l o g y o f m a j o r r i v e r d e l t a sa s f u n c t i o n s o f o c e a n w a v e a n d r i v e r d i s c h a r g e r e g im e s . B u l l. A m . A s s o c . P e t . G e o l . ,5 7 : 3 7 0 - - 3 9 8 .Y a l i n , S . a n d R u s s e ll , R . D . H . , 1 9 6 2 . S i m i l a r i t y i n s e d i m e n t t r a n s p o r t d u e t o w a v es . P r o c .8 t h C o n f . C o a s t a l E n g i n e e r i n g , p p . 1 5 1 - - 1 7 1 .